sum from n=5 to infinity of (7^n)/(8^n)

解答

n = 5 \sum \infty \frac{7 ^{n}}{8 ^{n}}

收敛

求解步骤

n = 5 \sum \infty \frac{7 ^{n}}{8 ^{n}}

n \to \infty lim (n (\frac{\frac{7 ^{n}}{8 ^{n}}}{\frac{7 ^{n + 1}}{8 ^{n + 1}}} - 1)) = \infty

L > 1,

由拉比判别法

= 收敛

\frac{d y}{d x} = 7^{x} ln (7) + \frac{2}{x ^{2} + 1}

\frac{d ^{3}}{d x ^{3}} (\frac{10}{x ^{2}})

\int (- e^{- x}) d x

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} - 3})

i = 0 \sum \infty (\frac{1}{3})^{i}